Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial

We apply the concept of slow surface-plasmon polariton standing-wave resonances to model the plasmon resonances which exist on split-ring resonators (U-shaped nanowires) forming the unit cell of a metamaterial at infrared frequencies. We compare the expected resonances predicted by the model with full electrodynamic three-dimensional simulations of the U-shaped nanowires for varying geometrical parameters and find a reasonably good agreement. We also consider how far-field dipolar coupling between unit-cells and near-field coupling between the U-shaped nanowire's arms should be taken into account. In addition, we study how the different resonances give rise to negative constitutive parameters for the metamaterial and adjust the geometrical parameters so that the second and third order slow-SPP standing-wave resonances of the U-shaped nanowires result in a double-negative behavior at far-infrared wavelengths without the need of further wires or particles. Finally, we study the effects of stacking N layers of such metamaterial, where each resonant mode splits into N normal mode resonances, showing different electric or magnetic responses. This simple stacked structure maintains the left-handed behavior, exhibiting backward wave propagation.